Problem: What do the following two equations represent? $-4x+5y = 3$ $-25x-20y = 3$
Explanation: Putting the first equation in $y = mx + b$ form gives: $-4x+5y = 3$ $5y = 4x+3$ $y = \dfrac{4}{5}x + \dfrac{3}{5}$ Putting the second equation in $y = mx + b$ form gives: $-25x-20y = 3$ $-20y = 25x+3$ $y = -\dfrac{5}{4}x - \dfrac{3}{20}$ The slopes are negative inverses of each other, so the lines are perpendicular.